MathSolver74
1) f(x) = x² sin x f ' (x) = 2x sin x + x² cos x
2) f(x) = cos x/(cos x + sin x) = ((-sin x)(cos x + sin x) - (cos x)(-sin x + cos x)) / (cos x + sin x)² = ((-sin x cos x - sin²x + cosx sin x - cos² x))/ (cos x + sin x)² = -1/(cos x + sin x)²
f ' (x) = 2x sin x + x² cos x
2) f(x) = cos x/(cos x + sin x)
= ((-sin x)(cos x + sin x) - (cos x)(-sin x + cos x)) / (cos x + sin x)²
= ((-sin x cos x - sin²x + cosx sin x - cos² x))/ (cos x + sin x)²
= -1/(cos x + sin x)²
3) f(x) = 5 cos 5x
f ' (x) = -25 sin 5x